Mathematics Root Calculator

Find square roots, cube roots, and nth roots with our mathematics root calculator. This tool helps you solve root equations quickly and accurately, with clear explanations and visualizations.

What is a Root Calculator?

A root calculator is a mathematical tool that helps you find the roots of numbers. The most common roots are square roots (√) and cube roots (∛), but you can also calculate higher-order roots like fourth roots or fifth roots.

Roots are inverse operations of exponents. For example, the square root of 16 is 4 because 4 × 4 = 16. Similarly, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Note: The root calculator can only find real roots. Complex roots (involving imaginary numbers) are not calculated by this tool.

How to Use the Root Calculator

Enter the number you want to find the root of in the "Number" field.
Select the type of root you want to calculate (square, cube, or nth root).
If you selected "nth root", enter the value of n in the additional field.
Click the "Calculate" button to see the result.
Use the "Reset" button to clear all fields and start over.

The calculator will display the result in the result panel below the form. You can also view a chart showing the relationship between the number and its root.

Formula

The formula for calculating roots depends on the type of root you're finding:

Square Root: √a = a^(1/2)

Cube Root: ∛a = a^(1/3)

Nth Root: ∜a = a^(1/n)

Where:

a is the number you want to find the root of
n is the order of the root (for nth root)

Examples

Example 1: Square Root

Find the square root of 25.

Using the formula: √25 = 25^(1/2) = 5

So, the square root of 25 is 5.

Example 2: Cube Root

Find the cube root of 64.

Using the formula: ∛64 = 64^(1/3) = 4

So, the cube root of 64 is 4.

Example 3: Nth Root

Find the fourth root of 16.

Using the formula: ∜16 = 16^(1/4) = 2

So, the fourth root of 16 is 2.

FAQ

What is the difference between a square root and a cube root?

A square root is the value that, when multiplied by itself, gives the original number. A cube root is the value that, when multiplied by itself three times, gives the original number.

Can I find the root of a negative number?

No, this calculator only finds real roots. Negative numbers have complex roots that involve imaginary numbers.

What is the difference between a square root and a fourth root?

A square root is the value that, when multiplied by itself, gives the original number. A fourth root is the value that, when multiplied by itself four times, gives the original number.